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manglu99
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Asked: 2023-02-23T08:44:31+00:00 In:

In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm,

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In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm,

Find the area of the shaded region. (Use π = 3.14)
NCERT Math’s Class 10 Chapter 12
Page No. 237
Exercise 12.3
Question No. 13

chapter 12class 10ncert maths
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      In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm,

      In A0AB,
      OB² = OA² + AB² ⇒ OB² = (20)² + (20)² ⇒ OB² = 400+ 400
      ⇒ OB² = 800 ⇒ OB = √800
      Radius of quadrant = 20√2 cm
      Area of quadrant
      = 90°/360° × πr² = 1/4 × π(20√2)²
      = 1/4 × 3.14 × 20√2 × 20√2 = 628 cm²
      Area of square
      = (Side)² = (20)² = 400 cm²
      Area of shaded region = Area of quadrant – Area of square
      = 628 – 400 = 228 cm²

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